Internal problem ID [3598]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 342.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
\[ \boxed {\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 126
dsolve((b*x+a)^2*diff(y(x),x)+c*y(x)^2+(b*x+a)*y(x)^3 = 0,y(x), singsol=all)
\[ \frac {\left (\sqrt {b}\, a +b^{\frac {3}{2}} x \right ) {\mathrm e}^{-\frac {\left (\left (b x +a +c \right ) y \left (x \right )+b \left (b x +a \right )\right ) \left (\left (-b x -a +c \right ) y \left (x \right )+b \left (b x +a \right )\right )}{2 y \left (x \right )^{2} \left (b x +a \right )^{2} b}}+\frac {c \sqrt {2}\, \sqrt {\pi }\, {\mathrm e}^{\frac {1}{2 b}} \operatorname {erf}\left (\frac {\sqrt {2}\, \left (c y \left (x \right )+b \left (b x +a \right )\right )}{2 \sqrt {b}\, y \left (x \right ) \left (b x +a \right )}\right )}{2}+b^{\frac {3}{2}} c_{1}}{b^{\frac {3}{2}}} = 0 \]
✓ Solution by Mathematica
Time used: 1.435 (sec). Leaf size: 149
DSolve[(a+b x)^2 y'[x]+c y[x]^2+(a+b x)y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {c}{\sqrt {-b (a+b x)^2}}=\frac {2 \exp \left (\frac {1}{2} \left (-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}\right )^2\right )}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]